The coalition government faces the first industrial uprising against its austerity measures today as up to 750,000 public servants strike over planned changes to their pensions.

A third of schools are expected to close and two-thirds of universities have cancelled lectures. Benefits will go unpaid, court cases will be postponed, police leave has been cancelled in London and airports are bracing themselves for backlogs at immigration.

Mark Serwotka, leader of the Public and Commercial Services union, said it was the most important strike in his union's history. "Everything we have ever worked for is under attack," he added.

The government was trying to avoid inflaming the situation . David Cameron told the Commons: "What we are proposing is fair: it is fair to taxpayers but it is also fair to the public sector because we want to continue strong public sector pensions."

He said Labour was avoiding the issue, accusing the party of being "paid for by the unions [so] they can't discuss the unions". None of the four striking unions, with members in schools, colleges, universities and the civil service, is affiliated to the Labour party.

Nearly every other union is poised to move towards strike action by the end of the year if the bitter standoff over public sector pension reforms is not resolved.

Roads in central London will shut as thousands of people march in demonstrations that will be echoed across the country. Police leave has been cancelled so officers can cover for striking police community support officers, call handlers on the 999 lines and security staff.

Some groups calling for peaceful civil disobedience are planning events in the capital. There were suggestions on the web that anarchists may target the events.

Downing Street said it believed only one in five of the 500,000 civil servants would strike and predicted that a third of England's 24,600 schools would close, a third would partially close and a third would be unaffected.

Nearly 8,000 state schools have confirmed that they will either close or reduce lessons. Liverpool will be the worst hit city, with three-quarters of schools affected. In Newcastle, 72% of schools will be short-staffed or closed and in Manchester and Birmingham around half are affected. Up to 20,000 teachers in private schools may also go on strike.

BAA said delays and disruption were possible at its airports, as up to 14,000 staff at the UK Border Agency affiliated to the PCS prepared to stage walkouts. UKBA advised airlines this week that passengers should rethink their travel plans amid fears of long queues at passport control, but then appeared to back away from that advice, saying it would work hard to keep delays to a minimum.

The PCS said it expected delays at the port of Dover and Heathrow, Manchester and Gatwick airports. Ryanair called on the government to allow the army or police to staff passport booths and customs desks and said what it called union "headbangers" should not be allowed to disrupt flight schedules.

The business secretary, Vince Cable, said: "I don't think the public will understand. The public view would be that we are negotiating and are willing to negotiate, so why would people be out on strike until that process has run its course?"

Cable said he was "optimistic" that pensions reform talks would succeed, saying: "Most trade unions are committed to negotiations. They asked for the talks and we are taking them seriously." He also played down the scale of strikes, pointing to the "relatively" small number of unions taking part today.

But Brendan Barber, the general secretary of the TUC, is to say that the strikes are "hardly surprising" considering the scale of the government's cuts to the public sector. "Nobody wants to see our schools and jobcentres closed. But our resolve is strong, our determination is absolute and we will see this through until we reach a just and fair settlement."

Both the unions and government are watching keenly to gauge the public tolerance to today's the disruption, to influence their future strategies. One senior Conservative source described the strike as a "test-case" of the strikes acknowledging that there are fears within government that the sustained strike action that some unions are threatening could ultimately damage the economic recovery. He said: "People are cautious, I'd say nervous. If there is a summer, autumn, winter of discontent the real worry is the effect on the economy. We're waiting to see where public opinion goes on this and the strategy is to be non-confrontational, make the argument to the public but not provoke the unions."

By one estimate the tTreasury could save £30m from the pay forfeited by the striking teachers today but business leaders warned that this was hugely outbalanced by the wider cost to the economy of hundreds of thousands of parents having to take the day off.

The British Chambers of Commerce said disruption will lead to many parents having to take the day off work to look after their children, losing them pay and hitting productivity.